# The project

Following on from the innovative links forged between contemporary art and the world of
science in the past few years, this project is the outcome of the collaboration between
The Association Subalpina Mathesis and the Mathematics Department of Turin University
which have the aim to realise a scientific dissemination project on a complex and difficult
topic as mathematical theorems.
For the Outreach section of the Euroscience Open Forum 2010, we would like to set up a
multimedia exhibition in which the relationship between art and science, based on the
principles of challenge and a reciprocal exchange of knowledge, will play a key role in the
process of informing the public, as well as allowing viewers to explore some of the most
interesting aspects of mathematics from new and stimulating points of view.

The exhibition

The interactive path of the exhibition aims to focusing on mathematics aspects both from
a technical point of view and from an artistic perspective. The visitors will have the
opportunity to approach and understand these complicated topics by comparing two
different “proofs” of every theorem: the artwork, created by the artist and the conceptual
and historical issues.
The scientific routes will present some examples of theorems and mathematical
statements that stimulate the curiosity of the visitors, aiming to deepening the topics and
illustrating how contemporary mathematics is a process in continue evolution and a
source of inspiration for scientists and artists.
The artistic path and the scientific path are complementary. For this reason researchers
and artists will cooperate in a challenging exchange of knowledge.
Therefore, the artistic and the scientific languages will merge with the objective to
stimulate curiosity towards art in people who are interested in mathematics and enable
people who are used to understand only art expression to approach mathematics.

**The scientific view**

__The exhibition will be articulated in four parts:__

The first part will open with the analysis of the Pythagora’s theorem
and some of its numerous proofs; next, there will be the Fermat theorem,
as well as other generalizations. The route will be completed by the
concept of irrationality of the square root of 2 – or the incommensurability
of the side and the diagonal of a square. These are themes that offer
many touch points with “famous” numbers, such as the golden ratio, and
their relationships with other branches of learning. Real numbers, which
include irrationals, are one of the main subjects both in Logic and
Foundation of Mathematics and in modern Mathematical Analysis.

The second part will deal with prime numbers: starting from the proof
of their infinity, known as the Euclid’s proof, the exhibition will
show other intriguing aspects of mathematical research, such as the
Goldbach conjecture and the Riemann hypothesis – mathematicians think
that both are possibly true but anyone has ever been able to find any
proof. The up-to-dateness of prime number theory is mainly related to
their use in cryptography and in public cipher systems.

The third part is meant to cope with the issue of classification of
surfaces and the bonds between the topological and differential properties
of a surface. The most important element of this part will be the Hairy
ball theorem, that has interesting applications in mathematics, in meteorology
and in computer-graphics. The hairy ball theorem states that you can’t
brush the hair on a fur-covered sphere so that the hair lie flat at
every point. The fourth part will be dedicated to proofs that use software
applications, such as the four colour theorem (already proved) and the
P versus NP problem, not proved but extremely important in fields such
as, for example, complexity-based cryptography. Such problem has wide
applications in fields such as the theory of algorithms, complexity
theory, data structures.

The artistic view

The artistic display will add another dimension to the scientific project and will help
visitors to understand these complex subjects, as well as offering a new and original
point of view.
The artists will be selected by the Accademia Albertina delle Belle arti and the Parco
d’Arte vivente PAV. The artists will create installations/artworks from a personal point of
view on a specific subject-matter, provided they respect the scientific content of the
application they choose. They will be supervised by researchers who will follow their
creation step by step and by important artists as Piero Gilardi and art critics as Franco
Torriani.